LMFDB - Embedded newform 6017.2.a.f.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.10704 q^{2} -1.55624 q^{3} +2.43961 q^{4} -0.464512 q^{5} +3.27907 q^{6} -0.781558 q^{7} -0.926282 q^{8} -0.578102 q^{9} +O(q^{10})$	\(q-2.10704 q^{2} -1.55624 q^{3} +2.43961 q^{4} -0.464512 q^{5} +3.27907 q^{6} -0.781558 q^{7} -0.926282 q^{8} -0.578102 q^{9} +0.978744 q^{10} -1.00000 q^{11} -3.79664 q^{12} -6.89190 q^{13} +1.64677 q^{14} +0.722894 q^{15} -2.92751 q^{16} +4.41736 q^{17} +1.21808 q^{18} +6.82809 q^{19} -1.13323 q^{20} +1.21630 q^{21} +2.10704 q^{22} -0.0938169 q^{23} +1.44152 q^{24} -4.78423 q^{25} +14.5215 q^{26} +5.56840 q^{27} -1.90670 q^{28} +6.75883 q^{29} -1.52317 q^{30} -9.92986 q^{31} +8.02095 q^{32} +1.55624 q^{33} -9.30755 q^{34} +0.363043 q^{35} -1.41034 q^{36} +1.09753 q^{37} -14.3871 q^{38} +10.7255 q^{39} +0.430269 q^{40} -10.0398 q^{41} -2.56278 q^{42} +10.8534 q^{43} -2.43961 q^{44} +0.268535 q^{45} +0.197676 q^{46} -12.6125 q^{47} +4.55593 q^{48} -6.38917 q^{49} +10.0806 q^{50} -6.87450 q^{51} -16.8136 q^{52} +3.80944 q^{53} -11.7328 q^{54} +0.464512 q^{55} +0.723943 q^{56} -10.6262 q^{57} -14.2411 q^{58} -0.976632 q^{59} +1.76358 q^{60} -3.58002 q^{61} +20.9226 q^{62} +0.451820 q^{63} -11.0454 q^{64} +3.20137 q^{65} -3.27907 q^{66} -10.4523 q^{67} +10.7767 q^{68} +0.146002 q^{69} -0.764945 q^{70} -2.15531 q^{71} +0.535485 q^{72} +2.99520 q^{73} -2.31254 q^{74} +7.44543 q^{75} +16.6579 q^{76} +0.781558 q^{77} -22.5990 q^{78} +4.36567 q^{79} +1.35986 q^{80} -6.93149 q^{81} +21.1543 q^{82} -2.51149 q^{83} +2.96729 q^{84} -2.05192 q^{85} -22.8686 q^{86} -10.5184 q^{87} +0.926282 q^{88} +2.79207 q^{89} -0.565814 q^{90} +5.38642 q^{91} -0.228877 q^{92} +15.4533 q^{93} +26.5751 q^{94} -3.17173 q^{95} -12.4826 q^{96} -1.81420 q^{97} +13.4622 q^{98} +0.578102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) $ 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.10704	−1.48990	−0.744951	−	0.667119i	$-0.767527\pi$
$2$	−2.10704	−1.48990	−0.744951	+	0.667119i	$0.767527\pi$
$3$	−1.55624	−0.898498	−0.449249	−	0.893406i	$-0.648308\pi$
$3$	−1.55624	−0.898498	−0.449249	+	0.893406i	$0.648308\pi$
$4$	2.43961	1.21981
$5$	−0.464512	−0.207736	−0.103868	−	0.994591i	$-0.533122\pi$
$5$	−0.464512	−0.207736	−0.103868	+	0.994591i	$0.533122\pi$
$6$	3.27907	1.33867
$7$	−0.781558	−0.295401	−0.147701	−	0.989032i	$-0.547187\pi$
$7$	−0.781558	−0.295401	−0.147701	+	0.989032i	$0.547187\pi$
$8$	−0.926282	−0.327490
$9$	−0.578102	−0.192701
$10$	0.978744	0.309506
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.79664	−1.09599
$13$	−6.89190	−1.91147	−0.955735	−	0.294229i	$-0.904937\pi$
$13$	−6.89190	−1.91147	−0.955735	+	0.294229i	$0.904937\pi$
$14$	1.64677	0.440119
$15$	0.722894	0.186650
$16$	−2.92751	−0.731879
$17$	4.41736	1.07137	0.535684	−	0.844419i	$-0.320054\pi$
$17$	4.41736	1.07137	0.535684	+	0.844419i	$0.320054\pi$
$18$	1.21808	0.287105
$19$	6.82809	1.56647	0.783236	−	0.621725i	$-0.213568\pi$
$19$	6.82809	1.56647	0.783236	+	0.621725i	$0.213568\pi$
$20$	−1.13323	−0.253398
$21$	1.21630	0.265418
$22$	2.10704	0.449222
$23$	−0.0938169	−0.0195622	−0.00978109	−	0.999952i	$-0.503113\pi$
$23$	−0.0938169	−0.0195622	−0.00978109	+	0.999952i	$0.503113\pi$
$24$	1.44152	0.294249
$25$	−4.78423	−0.956846
$26$	14.5215	2.84790
$27$	5.56840	1.07164
$28$	−1.90670	−0.360332
$29$	6.75883	1.25508	0.627541	−	0.778583i	$-0.284061\pi$
$29$	6.75883	1.25508	0.627541	+	0.778583i	$0.284061\pi$
$30$	−1.52317	−0.278091
$31$	−9.92986	−1.78345	−0.891727	−	0.452573i	$-0.850506\pi$
$31$	−9.92986	−1.78345	−0.891727	+	0.452573i	$0.850506\pi$
$32$	8.02095	1.41792
$33$	1.55624	0.270907
$34$	−9.30755	−1.59623
$35$	0.363043	0.0613654
$36$	−1.41034	−0.235057
$37$	1.09753	0.180433	0.0902165	−	0.995922i	$-0.471244\pi$
$37$	1.09753	0.180433	0.0902165	+	0.995922i	$0.471244\pi$
$38$	−14.3871	−2.33389
$39$	10.7255	1.71745
$40$	0.430269	0.0680314
$41$	−10.0398	−1.56796	−0.783980	−	0.620786i	$-0.786813\pi$
$41$	−10.0398	−1.56796	−0.783980	+	0.620786i	$0.786813\pi$
$42$	−2.56278	−0.395446
$43$	10.8534	1.65513	0.827566	−	0.561368i	$-0.189725\pi$
$43$	10.8534	1.65513	0.827566	+	0.561368i	$0.189725\pi$
$44$	−2.43961	−0.367786
$45$	0.268535	0.0400308
$46$	0.197676	0.0291457
$47$	−12.6125	−1.83973	−0.919865	−	0.392236i	$-0.871702\pi$
$47$	−12.6125	−1.83973	−0.919865	+	0.392236i	$0.871702\pi$
$48$	4.55593	0.657592
$49$	−6.38917	−0.912738
$50$	10.0806	1.42561
$51$	−6.87450	−0.962622
$52$	−16.8136	−2.33162
$53$	3.80944	0.523267	0.261634	−	0.965167i	$-0.415739\pi$
$53$	3.80944	0.523267	0.261634	+	0.965167i	$0.415739\pi$
$54$	−11.7328	−1.59664
$55$	0.464512	0.0626347
$56$	0.723943	0.0967410
$57$	−10.6262	−1.40747
$58$	−14.2411	−1.86995
$59$	−0.976632	−0.127147	−0.0635733	−	0.997977i	$-0.520250\pi$
$59$	−0.976632	−0.127147	−0.0635733	+	0.997977i	$0.520250\pi$
$60$	1.76358	0.227677
$61$	−3.58002	−0.458374	−0.229187	−	0.973382i	$-0.573607\pi$
$61$	−3.58002	−0.458374	−0.229187	+	0.973382i	$0.573607\pi$
$62$	20.9226	2.65717
$63$	0.451820	0.0569240
$64$	−11.0454	−1.38068
$65$	3.20137	0.397081
$66$	−3.27907	−0.403625
$67$	−10.4523	−1.27695	−0.638476	−	0.769641i	$-0.720435\pi$
$67$	−10.4523	−1.27695	−0.638476	+	0.769641i	$0.720435\pi$
$68$	10.7767	1.30686
$69$	0.146002	0.0175766
$70$	−0.764945	−0.0914285
$71$	−2.15531	−0.255789	−0.127894	−	0.991788i	$-0.540822\pi$
$71$	−2.15531	−0.255789	−0.127894	+	0.991788i	$0.540822\pi$
$72$	0.535485	0.0631075
$73$	2.99520	0.350562	0.175281	−	0.984518i	$-0.443917\pi$
$73$	2.99520	0.350562	0.175281	+	0.984518i	$0.443917\pi$
$74$	−2.31254	−0.268827
$75$	7.44543	0.859724
$76$	16.6579	1.91079
$77$	0.781558	0.0890668
$78$	−22.5990	−2.55884
$79$	4.36567	0.491176	0.245588	−	0.969374i	$-0.421019\pi$
$79$	4.36567	0.491176	0.245588	+	0.969374i	$0.421019\pi$
$80$	1.35986	0.152037
$81$	−6.93149	−0.770166
$82$	21.1543	2.33611
$83$	−2.51149	−0.275672	−0.137836	−	0.990455i	$-0.544015\pi$
$83$	−2.51149	−0.275672	−0.137836	+	0.990455i	$0.544015\pi$
$84$	2.96729	0.323758
$85$	−2.05192	−0.222561
$86$	−22.8686	−2.46598
$87$	−10.5184	−1.12769
$88$	0.926282	0.0987420
$89$	2.79207	0.295959	0.147979	−	0.988990i	$-0.452723\pi$
$89$	2.79207	0.295959	0.147979	+	0.988990i	$0.452723\pi$
$90$	−0.565814	−0.0596420
$91$	5.38642	0.564651
$92$	−0.228877	−0.0238621
$93$	15.4533	1.60243
$94$	26.5751	2.74102
$95$	−3.17173	−0.325412
$96$	−12.4826	−1.27400
$97$	−1.81420	−0.184204	−0.0921020	−	0.995750i	$-0.529359\pi$
$97$	−1.81420	−0.184204	−0.0921020	+	0.995750i	$0.529359\pi$
$98$	13.4622	1.35989
$99$	0.578102	0.0581014
$100$	−11.6717	−1.16717
$101$	14.4043	1.43328	0.716642	−	0.697441i	$-0.245678\pi$
$101$	14.4043	1.43328	0.716642	+	0.697441i	$0.245678\pi$
$102$	14.4848	1.43421
$103$	−1.45789	−0.143650	−0.0718249	−	0.997417i	$-0.522882\pi$
$103$	−1.45789	−0.143650	−0.0718249	+	0.997417i	$0.522882\pi$
$104$	6.38384	0.625987
$105$	−0.564984	−0.0551367
$106$	−8.02664	−0.779617
$107$	−13.0371	−1.26035	−0.630173	−	0.776454i	$-0.717016\pi$
$107$	−13.0371	−1.26035	−0.630173	+	0.776454i	$0.717016\pi$
$108$	13.5847	1.30719
$109$	12.1611	1.16482	0.582410	−	0.812895i	$-0.302110\pi$
$109$	12.1611	1.16482	0.582410	+	0.812895i	$0.302110\pi$
$110$	−0.978744	−0.0933196
$111$	−1.70803	−0.162119
$112$	2.28802	0.216198
$113$	2.11125	0.198610	0.0993049	−	0.995057i	$-0.468338\pi$
$113$	2.11125	0.198610	0.0993049	+	0.995057i	$0.468338\pi$
$114$	22.3898	2.09700
$115$	0.0435790	0.00406377
$116$	16.4889	1.53096
$117$	3.98422	0.368341
$118$	2.05780	0.189436
$119$	−3.45243	−0.316483
$120$	−0.669603	−0.0611261
$121$	1.00000	0.0909091
$122$	7.54323	0.682932
$123$	15.6244	1.40881
$124$	−24.2250	−2.17547
$125$	4.54489	0.406507
$126$	−0.952003	−0.0848112
$127$	−11.4929	−1.01983	−0.509915	−	0.860225i	$-0.670323\pi$
$127$	−11.4929	−1.01983	−0.509915	+	0.860225i	$0.670323\pi$
$128$	7.23124	0.639158
$129$	−16.8906	−1.48713
$130$	−6.74541	−0.591611
$131$	−0.477214	−0.0416944	−0.0208472	−	0.999783i	$-0.506636\pi$
$131$	−0.477214	−0.0416944	−0.0208472	+	0.999783i	$0.506636\pi$
$132$	3.79664	0.330455
$133$	−5.33655	−0.462738
$134$	22.0234	1.90253
$135$	−2.58659	−0.222618
$136$	−4.09172	−0.350862
$137$	−9.02273	−0.770864	−0.385432	−	0.922736i	$-0.625948\pi$
$137$	−9.02273	−0.770864	−0.385432	+	0.922736i	$0.625948\pi$
$138$	−0.307632	−0.0261874
$139$	−19.6593	−1.66748	−0.833742	−	0.552155i	$-0.813806\pi$
$139$	−19.6593	−1.66748	−0.833742	+	0.552155i	$0.813806\pi$
$140$	0.885684	0.0748540
$141$	19.6282	1.65299
$142$	4.54133	0.381100
$143$	6.89190	0.576330
$144$	1.69240	0.141033
$145$	−3.13955	−0.260726
$146$	−6.31101	−0.522303
$147$	9.94311	0.820094
$148$	2.67755	0.220093
$149$	−19.0518	−1.56079	−0.780394	−	0.625288i	$-0.784981\pi$
$149$	−19.0518	−1.56079	−0.780394	+	0.625288i	$0.784981\pi$
$150$	−15.6878	−1.28090
$151$	−10.6080	−0.863266	−0.431633	−	0.902049i	$-0.642062\pi$
$151$	−10.6080	−0.863266	−0.431633	+	0.902049i	$0.642062\pi$
$152$	−6.32474	−0.513004
$153$	−2.55368	−0.206453
$154$	−1.64677	−0.132701
$155$	4.61253	0.370488
$156$	26.1660	2.09496
$157$	16.8406	1.34403	0.672013	−	0.740539i	$-0.265430\pi$
$157$	16.8406	1.34403	0.672013	+	0.740539i	$0.265430\pi$
$158$	−9.19863	−0.731804
$159$	−5.92843	−0.470155
$160$	−3.72582	−0.294552
$161$	0.0733234	0.00577869
$162$	14.6049	1.14747
$163$	13.6243	1.06714	0.533569	−	0.845757i	$-0.320851\pi$
$163$	13.6243	1.06714	0.533569	+	0.845757i	$0.320851\pi$
$164$	−24.4933	−1.91261
$165$	−0.722894	−0.0562772
$166$	5.29181	0.410724
$167$	6.31044	0.488317	0.244158	−	0.969735i	$-0.421488\pi$
$167$	6.31044	0.488317	0.244158	+	0.969735i	$0.421488\pi$
$168$	−1.12663	−0.0869216
$169$	34.4983	2.65372
$170$	4.32347	0.331595
$171$	−3.94733	−0.301860
$172$	26.4782	2.01894
$173$	−17.0807	−1.29862	−0.649310	−	0.760524i	$-0.724942\pi$
$173$	−17.0807	−1.29862	−0.649310	+	0.760524i	$0.724942\pi$
$174$	22.1627	1.68015
$175$	3.73915	0.282653
$176$	2.92751	0.220670
$177$	1.51988	0.114241
$178$	−5.88300	−0.440949
$179$	−21.4178	−1.60084	−0.800421	−	0.599439i	$-0.795391\pi$
$179$	−21.4178	−1.60084	−0.800421	+	0.599439i	$0.795391\pi$
$180$	0.655121	0.0488299
$181$	−14.1806	−1.05404	−0.527018	−	0.849854i	$-0.676690\pi$
$181$	−14.1806	−1.05404	−0.527018	+	0.849854i	$0.676690\pi$
$182$	−11.3494	−0.841274
$183$	5.57138	0.411848
$184$	0.0869009	0.00640642
$185$	−0.509816	−0.0374824
$186$	−32.5607	−2.38746
$187$	−4.41736	−0.323029
$188$	−30.7697	−2.24411
$189$	−4.35203	−0.316564
$190$	6.68295	0.484832
$191$	−7.21785	−0.522265	−0.261133	−	0.965303i	$-0.584096\pi$
$191$	−7.21785	−0.522265	−0.261133	+	0.965303i	$0.584096\pi$
$192$	17.1894	1.24054
$193$	−7.13565	−0.513635	−0.256818	−	0.966460i	$-0.582674\pi$
$193$	−7.13565	−0.513635	−0.256818	+	0.966460i	$0.582674\pi$
$194$	3.82259	0.274446
$195$	−4.98211	−0.356776
$196$	−15.5871	−1.11336
$197$	0.844817	0.0601907	0.0300953	−	0.999547i	$-0.490419\pi$
$197$	0.844817	0.0601907	0.0300953	+	0.999547i	$0.490419\pi$
$198$	−1.21808	−0.0865654
$199$	−11.9017	−0.843692	−0.421846	−	0.906668i	$-0.638618\pi$
$199$	−11.9017	−0.843692	−0.421846	+	0.906668i	$0.638618\pi$
$200$	4.43154	0.313358
$201$	16.2664	1.14734
$202$	−30.3505	−2.13545
$203$	−5.28242	−0.370753
$204$	−16.7711	−1.17421
$205$	4.66362	0.325721
$206$	3.07182	0.214024
$207$	0.0542357	0.00376964
$208$	20.1761	1.39896
$209$	−6.82809	−0.472309
$210$	1.19044	0.0821483
$211$	−17.3963	−1.19761	−0.598804	−	0.800896i	$-0.704357\pi$
$211$	−17.3963	−1.19761	−0.598804	+	0.800896i	$0.704357\pi$
$212$	9.29357	0.638285
$213$	3.35420	0.229826
$214$	27.4697	1.87779
$215$	−5.04154	−0.343830
$216$	−5.15791	−0.350951
$217$	7.76076	0.526835
$218$	−25.6238	−1.73547
$219$	−4.66127	−0.314979
$220$	1.13323	0.0764022
$221$	−30.4440	−2.04789
$222$	3.59888	0.241541
$223$	24.5414	1.64342	0.821708	−	0.569908i	$-0.193021\pi$
$223$	24.5414	1.64342	0.821708	+	0.569908i	$0.193021\pi$
$224$	−6.26884	−0.418855
$225$	2.76577	0.184385
$226$	−4.44849	−0.295909
$227$	6.45910	0.428706	0.214353	−	0.976756i	$-0.431236\pi$
$227$	6.45910	0.428706	0.214353	+	0.976756i	$0.431236\pi$
$228$	−25.9238	−1.71684
$229$	21.5929	1.42690	0.713450	−	0.700706i	$-0.247132\pi$
$229$	21.5929	1.42690	0.713450	+	0.700706i	$0.247132\pi$
$230$	−0.0918227	−0.00605461
$231$	−1.21630	−0.0800264
$232$	−6.26058	−0.411027
$233$	−5.67337	−0.371675	−0.185837	−	0.982580i	$-0.559500\pi$
$233$	−5.67337	−0.371675	−0.185837	+	0.982580i	$0.559500\pi$
$234$	−8.39491	−0.548792
$235$	5.85867	0.382178
$236$	−2.38260	−0.155094
$237$	−6.79405	−0.441321
$238$	7.27440	0.471529
$239$	−20.4062	−1.31996	−0.659982	−	0.751281i	$-0.729436\pi$
$239$	−20.4062	−1.31996	−0.659982	+	0.751281i	$0.729436\pi$
$240$	−2.11628	−0.136605
$241$	−16.5604	−1.06675	−0.533374	−	0.845880i	$-0.679076\pi$
$241$	−16.5604	−1.06675	−0.533374	+	0.845880i	$0.679076\pi$
$242$	−2.10704	−0.135446
$243$	−5.91811	−0.379647
$244$	−8.73385	−0.559128
$245$	2.96784	0.189608
$246$	−32.9213	−2.09899
$247$	−47.0585	−2.99426
$248$	9.19785	0.584064
$249$	3.90850	0.247691
$250$	−9.57625	−0.605655
$251$	−0.221098	−0.0139556	−0.00697780	−	0.999976i	$-0.502221\pi$
$251$	−0.221098	−0.0139556	−0.00697780	+	0.999976i	$0.502221\pi$
$252$	1.10227	0.0694363
$253$	0.0938169	0.00589822
$254$	24.2160	1.51945
$255$	3.19328	0.199971
$256$	6.85434	0.428396
$257$	26.0049	1.62214	0.811070	−	0.584950i	$-0.198886\pi$
$257$	26.0049	1.62214	0.811070	+	0.584950i	$0.198886\pi$
$258$	35.5891	2.21568
$259$	−0.857784	−0.0533001
$260$	7.81010	0.484362
$261$	−3.90729	−0.241855
$262$	1.00551	0.0621205
$263$	17.1565	1.05791	0.528957	−	0.848648i	$-0.322583\pi$
$263$	17.1565	1.05791	0.528957	+	0.848648i	$0.322583\pi$
$264$	−1.44152	−0.0887195
$265$	−1.76953	−0.108701
$266$	11.2443	0.689434
$267$	−4.34514	−0.265919
$268$	−25.4996	−1.55764
$269$	−16.5038	−1.00626	−0.503128	−	0.864212i	$-0.667818\pi$
$269$	−16.5038	−1.00626	−0.503128	+	0.864212i	$0.667818\pi$
$270$	5.45004	0.331679
$271$	25.7543	1.56446	0.782230	−	0.622989i	$-0.214082\pi$
$271$	25.7543	1.56446	0.782230	+	0.622989i	$0.214082\pi$
$272$	−12.9319	−0.784111
$273$	−8.38259	−0.507338
$274$	19.0112	1.14851
$275$	4.78423	0.288500
$276$	0.356189	0.0214400
$277$	−22.2862	−1.33905	−0.669524	−	0.742791i	$-0.733502\pi$
$277$	−22.2862	−1.33905	−0.669524	+	0.742791i	$0.733502\pi$
$278$	41.4230	2.48439
$279$	5.74047	0.343673
$280$	−0.336280	−0.0200966
$281$	−1.63736	−0.0976765	−0.0488382	−	0.998807i	$-0.515552\pi$
$281$	−1.63736	−0.0976765	−0.0488382	+	0.998807i	$0.515552\pi$
$282$	−41.3574	−2.46280
$283$	12.1106	0.719899	0.359950	−	0.932972i	$-0.382794\pi$
$283$	12.1106	0.719899	0.359950	+	0.932972i	$0.382794\pi$
$284$	−5.25813	−0.312013
$285$	4.93598	0.292382
$286$	−14.5215	−0.858675
$287$	7.84672	0.463177
$288$	−4.63693	−0.273233
$289$	2.51308	0.147828
$290$	6.61516	0.388456
$291$	2.82334	0.165507
$292$	7.30713	0.427618
$293$	−10.8622	−0.634575	−0.317287	−	0.948329i	$-0.602772\pi$
$293$	−10.8622	−0.634575	−0.317287	+	0.948329i	$0.602772\pi$
$294$	−20.9505	−1.22186
$295$	0.453657	0.0264129
$296$	−1.01662	−0.0590900
$297$	−5.56840	−0.323111
$298$	40.1430	2.32542
$299$	0.646577	0.0373925
$300$	18.1640	1.04870
$301$	−8.48259	−0.488928
$302$	22.3515	1.28618
$303$	−22.4167	−1.28780
$304$	−19.9893	−1.14647
$305$	1.66296	0.0952207
$306$	5.38071	0.307595
$307$	29.5682	1.68755	0.843773	−	0.536701i	$-0.180330\pi$
$307$	29.5682	1.68755	0.843773	+	0.536701i	$0.180330\pi$
$308$	1.90670	0.108644
$309$	2.26883	0.129069
$310$	−9.71879	−0.551990
$311$	−30.3015	−1.71824	−0.859121	−	0.511773i	$-0.828989\pi$
$311$	−30.3015	−1.71824	−0.859121	+	0.511773i	$0.828989\pi$
$312$	−9.93483	−0.562449
$313$	−20.9506	−1.18420	−0.592099	−	0.805865i	$-0.701701\pi$
$313$	−20.9506	−1.18420	−0.592099	+	0.805865i	$0.701701\pi$
$314$	−35.4838	−2.00247
$315$	−0.209876	−0.0118252
$316$	10.6505	0.599139
$317$	0.351956	0.0197678	0.00988391	−	0.999951i	$-0.496854\pi$
$317$	0.351956	0.0197678	0.00988391	+	0.999951i	$0.496854\pi$
$318$	12.4914	0.700484
$319$	−6.75883	−0.378422
$320$	5.13073	0.286816
$321$	20.2890	1.13242
$322$	−0.154495	−0.00860968
$323$	30.1622	1.67827
$324$	−16.9102	−0.939453
$325$	32.9724	1.82898
$326$	−28.7069	−1.58993
$327$	−18.9256	−1.04659
$328$	9.29972	0.513491
$329$	9.85744	0.543458
$330$	1.52317	0.0838475
$331$	−24.3030	−1.33581	−0.667906	−	0.744246i	$-0.732809\pi$
$331$	−24.3030	−1.33581	−0.667906	+	0.744246i	$0.732809\pi$
$332$	−6.12707	−0.336267
$333$	−0.634484	−0.0347695
$334$	−13.2964	−0.727544
$335$	4.85522	0.265269
$336$	−3.56072	−0.194253
$337$	−33.2534	−1.81143	−0.905715	−	0.423886i	$-0.860666\pi$
$337$	−33.2534	−1.81143	−0.905715	+	0.423886i	$0.860666\pi$
$338$	−72.6893	−3.95378
$339$	−3.28563	−0.178451
$340$	−5.00588	−0.271482
$341$	9.92986	0.537732
$342$	8.31718	0.449742
$343$	10.4644	0.565025
$344$	−10.0533	−0.542039
$345$	−0.0678196	−0.00365129
$346$	35.9897	1.93482
$347$	33.3486	1.79025	0.895124	−	0.445817i	$-0.147087\pi$
$347$	33.3486	1.79025	0.895124	+	0.445817i	$0.147087\pi$
$348$	−25.6608	−1.37556
$349$	30.1214	1.61236	0.806181	−	0.591670i	$-0.201531\pi$
$349$	30.1214	1.61236	0.806181	+	0.591670i	$0.201531\pi$
$350$	−7.87854	−0.421126
$351$	−38.3769	−2.04841
$352$	−8.02095	−0.427518
$353$	5.82745	0.310164	0.155082	−	0.987902i	$-0.450436\pi$
$353$	5.82745	0.310164	0.155082	+	0.987902i	$0.450436\pi$
$354$	−3.20244	−0.170208
$355$	1.00117	0.0531365
$356$	6.81157	0.361012
$357$	5.37282	0.284360
$358$	45.1281	2.38510
$359$	−23.3824	−1.23408	−0.617038	−	0.786933i	$-0.711668\pi$
$359$	−23.3824	−1.23408	−0.617038	+	0.786933i	$0.711668\pi$
$360$	−0.248739	−0.0131097
$361$	27.6228	1.45383
$362$	29.8791	1.57041
$363$	−1.55624	−0.0816817
$364$	13.1408	0.688765
$365$	−1.39131	−0.0728243
$366$	−11.7391	−0.613613
$367$	8.32041	0.434322	0.217161	−	0.976136i	$-0.430320\pi$
$367$	8.32041	0.434322	0.217161	+	0.976136i	$0.430320\pi$
$368$	0.274650	0.0143171
$369$	5.80405	0.302147
$370$	1.07420	0.0558451
$371$	−2.97730	−0.154574
$372$	37.7000	1.95466
$373$	32.5387	1.68479	0.842396	−	0.538860i	$-0.181145\pi$
$373$	32.5387	1.68479	0.842396	+	0.538860i	$0.181145\pi$
$374$	9.30755	0.481282
$375$	−7.07296	−0.365246
$376$	11.6828	0.602493
$377$	−46.5812	−2.39905
$378$	9.16990	0.471649
$379$	34.7857	1.78682	0.893411	−	0.449239i	$-0.148305\pi$
$379$	34.7857	1.78682	0.893411	+	0.449239i	$0.148305\pi$
$380$	−7.73779	−0.396940
$381$	17.8858	0.916315
$382$	15.2083	0.778123
$383$	17.7180	0.905347	0.452673	−	0.891676i	$-0.350470\pi$
$383$	17.7180	0.905347	0.452673	+	0.891676i	$0.350470\pi$
$384$	−11.2536	−0.574282
$385$	−0.363043	−0.0185024
$386$	15.0351	0.765266
$387$	−6.27439	−0.318945
$388$	−4.42594	−0.224693
$389$	−14.9057	−0.755749	−0.377875	−	0.925857i	$-0.623345\pi$
$389$	−14.9057	−0.755749	−0.377875	+	0.925857i	$0.623345\pi$
$390$	10.4975	0.531562
$391$	−0.414423	−0.0209583
$392$	5.91817	0.298913
$393$	0.742661	0.0374623
$394$	−1.78006	−0.0896782
$395$	−2.02790	−0.102035
$396$	1.41034	0.0708725
$397$	9.74094	0.488884	0.244442	−	0.969664i	$-0.421395\pi$
$397$	9.74094	0.488884	0.244442	+	0.969664i	$0.421395\pi$
$398$	25.0774	1.25702
$399$	8.30498	0.415769
$400$	14.0059	0.700295
$401$	−5.39741	−0.269534	−0.134767	−	0.990877i	$-0.543029\pi$
$401$	−5.39741	−0.269534	−0.134767	+	0.990877i	$0.543029\pi$
$402$	−34.2738	−1.70942
$403$	68.4356	3.40902
$404$	35.1410	1.74833
$405$	3.21976	0.159991
$406$	11.1303	0.552385
$407$	−1.09753	−0.0544026
$408$	6.36772	0.315249
$409$	12.9682	0.641235	0.320618	−	0.947209i	$-0.396110\pi$
$409$	12.9682	0.641235	0.320618	+	0.947209i	$0.396110\pi$
$410$	−9.82643	−0.485293
$411$	14.0416	0.692620
$412$	−3.55668	−0.175225
$413$	0.763295	0.0375593
$414$	−0.114277	−0.00561640
$415$	1.16662	0.0572670
$416$	−55.2796	−2.71031
$417$	30.5948	1.49823
$418$	14.3871	0.703694
$419$	38.7312	1.89214	0.946070	−	0.323961i	$-0.105015\pi$
$419$	38.7312	1.89214	0.946070	+	0.323961i	$0.105015\pi$
$420$	−1.37834	−0.0672562
$421$	−7.34889	−0.358163	−0.179081	−	0.983834i	$-0.557313\pi$
$421$	−7.34889	−0.358163	−0.179081	+	0.983834i	$0.557313\pi$
$422$	36.6546	1.78432
$423$	7.29134	0.354517
$424$	−3.52862	−0.171365
$425$	−21.1337	−1.02513
$426$	−7.06742	−0.342418
$427$	2.79799	0.135404
$428$	−31.8056	−1.53738
$429$	−10.7255	−0.517831
$430$	10.6227	0.512273
$431$	27.3475	1.31728	0.658640	−	0.752458i	$-0.271132\pi$
$431$	27.3475	1.31728	0.658640	+	0.752458i	$0.271132\pi$
$432$	−16.3016	−0.784310
$433$	−8.25871	−0.396888	−0.198444	−	0.980112i	$-0.563589\pi$
$433$	−8.25871	−0.396888	−0.198444	+	0.980112i	$0.563589\pi$
$434$	−16.3522	−0.784932
$435$	4.88591	0.234262
$436$	29.6683	1.42085
$437$	−0.640590	−0.0306436
$438$	9.82147	0.469288
$439$	−2.96070	−0.141307	−0.0706533	−	0.997501i	$-0.522508\pi$
$439$	−2.96070	−0.141307	−0.0706533	+	0.997501i	$0.522508\pi$
$440$	−0.430269	−0.0205123
$441$	3.69359	0.175885
$442$	64.1467	3.05115
$443$	2.03486	0.0966791	0.0483395	−	0.998831i	$-0.484607\pi$
$443$	2.03486	0.0966791	0.0483395	+	0.998831i	$0.484607\pi$
$444$	−4.16692	−0.197753
$445$	−1.29695	−0.0614813
$446$	−51.7098	−2.44853
$447$	29.6493	1.40237
$448$	8.63264	0.407854
$449$	7.46400	0.352248	0.176124	−	0.984368i	$-0.443644\pi$
$449$	7.46400	0.352248	0.176124	+	0.984368i	$0.443644\pi$
$450$	−5.82759	−0.274715
$451$	10.0398	0.472758
$452$	5.15064	0.242266
$453$	16.5086	0.775643
$454$	−13.6096	−0.638729
$455$	−2.50206	−0.117298
$456$	9.84284	0.460933
$457$	−15.0131	−0.702284	−0.351142	−	0.936322i	$-0.614207\pi$
$457$	−15.0131	−0.702284	−0.351142	+	0.936322i	$0.614207\pi$
$458$	−45.4971	−2.12594
$459$	24.5976	1.14812
$460$	0.106316	0.00495701
$461$	−1.46451	−0.0682089	−0.0341044	−	0.999418i	$-0.510858\pi$
$461$	−1.46451	−0.0682089	−0.0341044	+	0.999418i	$0.510858\pi$
$462$	2.56278	0.119231
$463$	11.5876	0.538522	0.269261	−	0.963067i	$-0.413221\pi$
$463$	11.5876	0.538522	0.269261	+	0.963067i	$0.413221\pi$
$464$	−19.7866	−0.918568
$465$	−7.17823	−0.332882
$466$	11.9540	0.553759
$467$	−35.7088	−1.65241	−0.826204	−	0.563372i	$-0.809504\pi$
$467$	−35.7088	−1.65241	−0.826204	+	0.563372i	$0.809504\pi$
$468$	9.71996	0.449305
$469$	8.16909	0.377213
$470$	−12.3445	−0.569407
$471$	−26.2081	−1.20761
$472$	0.904636	0.0416393
$473$	−10.8534	−0.499041
$474$	14.3153	0.657524
$475$	−32.6672	−1.49887
$476$	−8.42258	−0.386048
$477$	−2.20225	−0.100834
$478$	42.9966	1.96662
$479$	21.5204	0.983291	0.491646	−	0.870795i	$-0.336396\pi$
$479$	21.5204	0.983291	0.491646	+	0.870795i	$0.336396\pi$
$480$	5.79829	0.264655
$481$	−7.56407	−0.344892
$482$	34.8933	1.58935
$483$	−0.114109	−0.00519215
$484$	2.43961	0.110892
$485$	0.842716	0.0382658
$486$	12.4697	0.565636
$487$	26.6710	1.20858	0.604289	−	0.796766i	$-0.293457\pi$
$487$	26.6710	1.20858	0.604289	+	0.796766i	$0.293457\pi$
$488$	3.31610	0.150113
$489$	−21.2027	−0.958821
$490$	−6.25336	−0.282498
$491$	−12.2152	−0.551266	−0.275633	−	0.961263i	$-0.588888\pi$
$491$	−12.2152	−0.551266	−0.275633	+	0.961263i	$0.588888\pi$
$492$	38.1176	1.71847
$493$	29.8562	1.34465
$494$	99.1542	4.46116
$495$	−0.268535	−0.0120697
$496$	29.0698	1.30527
$497$	1.68450	0.0755603
$498$	−8.23536	−0.369035
$499$	29.7420	1.33144	0.665718	−	0.746203i	$-0.268125\pi$
$499$	29.7420	1.33144	0.665718	+	0.746203i	$0.268125\pi$
$500$	11.0878	0.495860
$501$	−9.82060	−0.438752
$502$	0.465863	0.0207925
$503$	24.2720	1.08224	0.541119	−	0.840946i	$-0.318001\pi$
$503$	24.2720	1.08224	0.541119	+	0.840946i	$0.318001\pi$
$504$	−0.418513	−0.0186420
$505$	−6.69097	−0.297744
$506$	−0.197676	−0.00878776
$507$	−53.6878	−2.38436
$508$	−28.0382	−1.24399
$509$	5.90079	0.261548	0.130774	−	0.991412i	$-0.458254\pi$
$509$	5.90079	0.261548	0.130774	+	0.991412i	$0.458254\pi$
$510$	−6.72837	−0.297937
$511$	−2.34093	−0.103556
$512$	−28.9049	−1.27743
$513$	38.0216	1.67869
$514$	−54.7933	−2.41683
$515$	0.677205	0.0298412
$516$	−41.2065	−1.81402
$517$	12.6125	0.554699
$518$	1.80738	0.0794119
$519$	26.5817	1.16681
$520$	−2.96537	−0.130040
$521$	−39.2608	−1.72005	−0.860024	−	0.510253i	$-0.829552\pi$
$521$	−39.2608	−1.72005	−0.860024	+	0.510253i	$0.829552\pi$
$522$	8.23281	0.360340
$523$	40.9889	1.79232	0.896160	−	0.443731i	$-0.146345\pi$
$523$	40.9889	1.79232	0.896160	+	0.443731i	$0.146345\pi$
$524$	−1.16422	−0.0508590
$525$	−5.81904	−0.253964
$526$	−36.1494	−1.57619
$527$	−43.8638	−1.91074
$528$	−4.55593	−0.198271
$529$	−22.9912	−0.999617
$530$	3.72847	0.161954
$531$	0.564593	0.0245012
$532$	−13.0191	−0.564451
$533$	69.1936	2.99711
$534$	9.15539	0.396192
$535$	6.05590	0.261819
$536$	9.68179	0.418189
$537$	33.3313	1.43835
$538$	34.7742	1.49922
$539$	6.38917	0.275201
$540$	−6.31027	−0.271551
$541$	31.8812	1.37068	0.685340	−	0.728224i	$-0.259654\pi$
$541$	31.8812	1.37068	0.685340	+	0.728224i	$0.259654\pi$
$542$	−54.2652	−2.33089
$543$	22.0685	0.947050
$544$	35.4314	1.51911
$545$	−5.64896	−0.241975
$546$	17.6625	0.755883
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−22.0120	−0.940305
$549$	2.06961	0.0883290
$550$	−10.0806	−0.429836
$551$	46.1499	1.96605
$552$	−0.135239	−0.00575616
$553$	−3.41202	−0.145094
$554$	46.9579	1.99505
$555$	0.793398	0.0336779
$556$	−47.9612	−2.03401
$557$	−23.6530	−1.00221	−0.501104	−	0.865387i	$-0.667073\pi$
$557$	−23.6530	−1.00221	−0.501104	+	0.865387i	$0.667073\pi$
$558$	−12.0954	−0.512039
$559$	−74.8008	−3.16373
$560$	−1.06281	−0.0449120
$561$	6.87450	0.290241
$562$	3.44997	0.145528
$563$	−20.9677	−0.883681	−0.441841	−	0.897094i	$-0.645674\pi$
$563$	−20.9677	−0.883681	−0.441841	+	0.897094i	$0.645674\pi$
$564$	47.8853	2.01633
$565$	−0.980701	−0.0412584
$566$	−25.5175	−1.07258
$567$	5.41737	0.227508
$568$	1.99643	0.0837683
$569$	−27.5476	−1.15485	−0.577427	−	0.816442i	$-0.695943\pi$
$569$	−27.5476	−1.15485	−0.577427	+	0.816442i	$0.695943\pi$
$570$	−10.4003	−0.435621
$571$	−29.0532	−1.21584	−0.607920	−	0.793999i	$-0.707996\pi$
$571$	−29.0532	−1.21584	−0.607920	+	0.793999i	$0.707996\pi$
$572$	16.8136	0.703011
$573$	11.2327	0.469254
$574$	−16.5333	−0.690088
$575$	0.448842	0.0187180
$576$	6.38538	0.266058
$577$	12.7582	0.531131	0.265565	−	0.964093i	$-0.414441\pi$
$577$	12.7582	0.531131	0.265565	+	0.964093i	$0.414441\pi$
$578$	−5.29517	−0.220250
$579$	11.1048	0.461501
$580$	−7.65929	−0.318035
$581$	1.96288	0.0814339
$582$	−5.94888	−0.246589
$583$	−3.80944	−0.157771
$584$	−2.77440	−0.114806
$585$	−1.85072	−0.0765177
$586$	22.8870	0.945454
$587$	2.22645	0.0918954	0.0459477	−	0.998944i	$-0.485369\pi$
$587$	2.22645	0.0918954	0.0459477	+	0.998944i	$0.485369\pi$
$588$	24.2573	1.00036
$589$	−67.8020	−2.79373
$590$	−0.955872	−0.0393526
$591$	−1.31474	−0.0540812
$592$	−3.21304	−0.132055
$593$	−28.6928	−1.17827	−0.589136	−	0.808034i	$-0.700532\pi$
$593$	−28.6928	−1.17827	−0.589136	+	0.808034i	$0.700532\pi$
$594$	11.7328	0.481404
$595$	1.60369	0.0657449
$596$	−46.4791	−1.90386
$597$	18.5220	0.758056
$598$	−1.36236	−0.0557112
$599$	19.1236	0.781371	0.390685	−	0.920524i	$-0.372238\pi$
$599$	19.1236	0.781371	0.390685	+	0.920524i	$0.372238\pi$
$600$	−6.89657	−0.281551
$601$	15.6066	0.636607	0.318303	−	0.947989i	$-0.396887\pi$
$601$	15.6066	0.636607	0.318303	+	0.947989i	$0.396887\pi$
$602$	17.8731	0.728455
$603$	6.04250	0.246070
$604$	−25.8794	−1.05302
$605$	−0.464512	−0.0188851
$606$	47.2328	1.91870
$607$	36.9665	1.50042	0.750212	−	0.661197i	$-0.229951\pi$
$607$	36.9665	1.50042	0.750212	+	0.661197i	$0.229951\pi$
$608$	54.7678	2.22113
$609$	8.22074	0.333121
$610$	−3.50392	−0.141870
$611$	86.9245	3.51659
$612$	−6.23000	−0.251833
$613$	−8.44792	−0.341208	−0.170604	−	0.985340i	$-0.554572\pi$
$613$	−8.44792	−0.341208	−0.170604	+	0.985340i	$0.554572\pi$
$614$	−62.3013	−2.51428
$615$	−7.25774	−0.292660
$616$	−0.723943	−0.0291685
$617$	−19.2430	−0.774694	−0.387347	−	0.921934i	$-0.626609\pi$
$617$	−19.2430	−0.774694	−0.387347	+	0.921934i	$0.626609\pi$
$618$	−4.78051	−0.192300
$619$	−21.6280	−0.869302	−0.434651	−	0.900599i	$-0.643128\pi$
$619$	−21.6280	−0.869302	−0.434651	+	0.900599i	$0.643128\pi$
$620$	11.2528	0.451923
$621$	−0.522410	−0.0209636
$622$	63.8465	2.56001
$623$	−2.18217	−0.0874266
$624$	−31.3990	−1.25697
$625$	21.8100	0.872400
$626$	44.1438	1.76434
$627$	10.6262	0.424369
$628$	41.0846	1.63945
$629$	4.84819	0.193310
$630$	0.442216	0.0176183
$631$	32.1437	1.27962	0.639810	−	0.768533i	$-0.279013\pi$
$631$	32.1437	1.27962	0.639810	+	0.768533i	$0.279013\pi$
$632$	−4.04384	−0.160855
$633$	27.0728	1.07605
$634$	−0.741585	−0.0294521
$635$	5.33858	0.211855
$636$	−14.4631	−0.573498
$637$	44.0335	1.74467
$638$	14.2411	0.563811
$639$	1.24599	0.0492906
$640$	−3.35900	−0.132776
$641$	21.9280	0.866105	0.433052	−	0.901369i	$-0.357437\pi$
$641$	21.9280	0.866105	0.433052	+	0.901369i	$0.357437\pi$
$642$	−42.7496	−1.68719
$643$	27.2923	1.07630	0.538151	−	0.842848i	$-0.319123\pi$
$643$	27.2923	1.07630	0.538151	+	0.842848i	$0.319123\pi$
$644$	0.178881	0.00704889
$645$	7.84587	0.308931
$646$	−63.5528	−2.50045
$647$	30.0400	1.18099	0.590497	−	0.807040i	$-0.298932\pi$
$647$	30.0400	1.18099	0.590497	+	0.807040i	$0.298932\pi$
$648$	6.42052	0.252222
$649$	0.976632	0.0383362
$650$	−69.4742	−2.72500
$651$	−12.0776	−0.473360
$652$	33.2380	1.30170
$653$	−18.4555	−0.722219	−0.361109	−	0.932523i	$-0.617602\pi$
$653$	−18.4555	−0.722219	−0.361109	+	0.932523i	$0.617602\pi$
$654$	39.8770	1.55931
$655$	0.221671	0.00866141
$656$	29.3918	1.14756
$657$	−1.73153	−0.0675535
$658$	−20.7700	−0.809700
$659$	11.9488	0.465461	0.232730	−	0.972541i	$-0.425234\pi$
$659$	11.9488	0.465461	0.232730	+	0.972541i	$0.425234\pi$
$660$	−1.76358	−0.0686473
$661$	23.3109	0.906688	0.453344	−	0.891336i	$-0.350231\pi$
$661$	23.3109	0.906688	0.453344	+	0.891336i	$0.350231\pi$
$662$	51.2073	1.99023
$663$	47.3784	1.84002
$664$	2.32635	0.0902799
$665$	2.47889	0.0961272
$666$	1.33688	0.0518032
$667$	−0.634092	−0.0245521
$668$	15.3950	0.595652
$669$	−38.1925	−1.47661
$670$	−10.2301	−0.395225
$671$	3.58002	0.138205
$672$	9.75585	0.376340
$673$	−23.8973	−0.921173	−0.460586	−	0.887615i	$-0.652361\pi$
$673$	−23.8973	−0.921173	−0.460586	+	0.887615i	$0.652361\pi$
$674$	70.0663	2.69885
$675$	−26.6405	−1.02539
$676$	84.1625	3.23702
$677$	−16.1862	−0.622084	−0.311042	−	0.950396i	$-0.600678\pi$
$677$	−16.1862	−0.622084	−0.311042	+	0.950396i	$0.600678\pi$
$678$	6.92294	0.265874
$679$	1.41790	0.0544141
$680$	1.90065	0.0728867
$681$	−10.0519	−0.385191
$682$	−20.9226	−0.801168
$683$	−20.6285	−0.789328	−0.394664	−	0.918826i	$-0.629139\pi$
$683$	−20.6285	−0.789328	−0.394664	+	0.918826i	$0.629139\pi$
$684$	−9.62996	−0.368211
$685$	4.19116	0.160136
$686$	−22.0489	−0.841832
$687$	−33.6038	−1.28207
$688$	−31.7736	−1.21136
$689$	−26.2543	−1.00021
$690$	0.142899	0.00544006
$691$	−21.6319	−0.822915	−0.411457	−	0.911429i	$-0.634980\pi$
$691$	−21.6319	−0.822915	−0.411457	+	0.911429i	$0.634980\pi$
$692$	−41.6703	−1.58407
$693$	−0.451820	−0.0171632
$694$	−70.2669	−2.66729
$695$	9.13199	0.346396
$696$	9.74299	0.369307
$697$	−44.3496	−1.67986
$698$	−63.4669	−2.40226
$699$	8.82916	0.333949
$700$	9.12209	0.344783
$701$	6.73632	0.254427	0.127214	−	0.991875i	$-0.459397\pi$
$701$	6.73632	0.254427	0.127214	+	0.991875i	$0.459397\pi$
$702$	80.8616	3.05192
$703$	7.49404	0.282643
$704$	11.0454	0.416290
$705$	−9.11753	−0.343386
$706$	−12.2787	−0.462113
$707$	−11.2578	−0.423394
$708$	3.70792	0.139352
$709$	2.95332	0.110914	0.0554571	−	0.998461i	$-0.482338\pi$
$709$	2.95332	0.110914	0.0554571	+	0.998461i	$0.482338\pi$
$710$	−2.10950	−0.0791681
$711$	−2.52380	−0.0946499
$712$	−2.58624	−0.0969236
$713$	0.931588	0.0348883
$714$	−11.3207	−0.423668
$715$	−3.20137	−0.119724
$716$	−52.2511	−1.95272
$717$	31.7570	1.18599
$718$	49.2677	1.83865
$719$	−4.80117	−0.179053	−0.0895267	−	0.995984i	$-0.528535\pi$
$719$	−4.80117	−0.179053	−0.0895267	+	0.995984i	$0.528535\pi$
$720$	−0.786140	−0.0292977
$721$	1.13942	0.0424343
$722$	−58.2024	−2.16607
$723$	25.7720	0.958471
$724$	−34.5952	−1.28572
$725$	−32.3358	−1.20092
$726$	3.27907	0.121698
$727$	35.2737	1.30823	0.654115	−	0.756395i	$-0.273041\pi$
$727$	35.2737	1.30823	0.654115	+	0.756395i	$0.273041\pi$
$728$	−4.98935	−0.184917
$729$	30.0045	1.11128
$730$	2.93154	0.108501
$731$	47.9435	1.77325
$732$	13.5920	0.502375
$733$	32.5383	1.20183	0.600915	−	0.799313i	$-0.294803\pi$
$733$	32.5383	1.20183	0.600915	+	0.799313i	$0.294803\pi$
$734$	−17.5314	−0.647097
$735$	−4.61869	−0.170363
$736$	−0.752501	−0.0277375
$737$	10.4523	0.385016
$738$	−12.2294	−0.450169
$739$	−23.1591	−0.851922	−0.425961	−	0.904741i	$-0.640064\pi$
$739$	−23.1591	−0.851922	−0.425961	+	0.904741i	$0.640064\pi$
$740$	−1.24375	−0.0457213
$741$	73.2346	2.69034
$742$	6.27329	0.230300
$743$	48.0380	1.76235	0.881173	−	0.472795i	$-0.156755\pi$
$743$	48.0380	1.76235	0.881173	+	0.472795i	$0.156755\pi$
$744$	−14.3141	−0.524780
$745$	8.84980	0.324232
$746$	−68.5603	−2.51017
$747$	1.45190	0.0531222
$748$	−10.7767	−0.394033
$749$	10.1893	0.372308
$750$	14.9030	0.544180
$751$	−26.7033	−0.974416	−0.487208	−	0.873286i	$-0.661985\pi$
$751$	−26.7033	−0.974416	−0.487208	+	0.873286i	$0.661985\pi$
$752$	36.9234	1.34646
$753$	0.344083	0.0125391
$754$	98.1483	3.57435
$755$	4.92754	0.179331
$756$	−10.6173	−0.386146
$757$	19.3461	0.703145	0.351573	−	0.936161i	$-0.385647\pi$
$757$	19.3461	0.703145	0.351573	+	0.936161i	$0.385647\pi$
$758$	−73.2949	−2.66219
$759$	−0.146002	−0.00529954
$760$	2.93791	0.106569
$761$	3.47525	0.125978	0.0629888	−	0.998014i	$-0.479937\pi$
$761$	3.47525	0.125978	0.0629888	+	0.998014i	$0.479937\pi$
$762$	−37.6860	−1.36522
$763$	−9.50458	−0.344089
$764$	−17.6088	−0.637062
$765$	1.18622	0.0428877
$766$	−37.3325	−1.34888
$767$	6.73085	0.243037
$768$	−10.6670	−0.384913
$769$	−14.3148	−0.516207	−0.258103	−	0.966117i	$-0.583097\pi$
$769$	−14.3148	−0.516207	−0.258103	+	0.966117i	$0.583097\pi$
$770$	0.764945	0.0275667
$771$	−40.4699	−1.45749
$772$	−17.4082	−0.626536
$773$	35.2376	1.26741	0.633705	−	0.773575i	$-0.281533\pi$
$773$	35.2376	1.26741	0.633705	+	0.773575i	$0.281533\pi$
$774$	13.2204	0.475197
$775$	47.5067	1.70649
$776$	1.68046	0.0603250
$777$	1.33492	0.0478901
$778$	31.4069	1.12599
$779$	−68.5529	−2.45616
$780$	−12.1544	−0.435198
$781$	2.15531	0.0771232
$782$	0.873206	0.0312258
$783$	37.6359	1.34500
$784$	18.7044	0.668013
$785$	−7.82266	−0.279203
$786$	−1.56482	−0.0558151
$787$	22.2012	0.791386	0.395693	−	0.918383i	$-0.370505\pi$
$787$	22.2012	0.791386	0.395693	+	0.918383i	$0.370505\pi$
$788$	2.06103	0.0734210
$789$	−26.6997	−0.950534
$790$	4.27287	0.152022
$791$	−1.65007	−0.0586696
$792$	−0.535485	−0.0190276
$793$	24.6731	0.876168
$794$	−20.5245	−0.728389
$795$	2.75382	0.0976680
$796$	−29.0356	−1.02914
$797$	16.1029	0.570395	0.285197	−	0.958469i	$-0.407941\pi$
$797$	16.1029	0.570395	0.285197	+	0.958469i	$0.407941\pi$
$798$	−17.4989	−0.619455
$799$	−55.7142	−1.97103
$800$	−38.3741	−1.35673
$801$	−1.61410	−0.0570314
$802$	11.3726	0.401579
$803$	−2.99520	−0.105698
$804$	39.6836	1.39953
$805$	−0.0340596	−0.00120044
$806$	−144.196	−5.07910
$807$	25.6840	0.904120
$808$	−13.3425	−0.469386
$809$	14.6650	0.515593	0.257796	−	0.966199i	$-0.417004\pi$
$809$	14.6650	0.515593	0.257796	+	0.966199i	$0.417004\pi$
$810$	−6.78416	−0.238371
$811$	−16.3449	−0.573948	−0.286974	−	0.957938i	$-0.592649\pi$
$811$	−16.3449	−0.573948	−0.286974	+	0.957938i	$0.592649\pi$
$812$	−12.8871	−0.452247
$813$	−40.0800	−1.40567
$814$	2.31254	0.0810545
$815$	−6.32864	−0.221683
$816$	20.1252	0.704522
$817$	74.1082	2.59272
$818$	−27.3245	−0.955377
$819$	−3.11390	−0.108809
$820$	11.3774	0.397317
$821$	26.5610	0.926986	0.463493	−	0.886101i	$-0.346596\pi$
$821$	26.5610	0.926986	0.463493	+	0.886101i	$0.346596\pi$
$822$	−29.5861	−1.03194
$823$	−9.25481	−0.322602	−0.161301	−	0.986905i	$-0.551569\pi$
$823$	−9.25481	−0.322602	−0.161301	+	0.986905i	$0.551569\pi$
$824$	1.35041	0.0470439
$825$	−7.44543	−0.259217
$826$	−1.60829	−0.0559596
$827$	28.1400	0.978524	0.489262	−	0.872137i	$-0.337266\pi$
$827$	28.1400	0.978524	0.489262	+	0.872137i	$0.337266\pi$
$828$	0.132314	0.00459824
$829$	46.1754	1.60374	0.801868	−	0.597501i	$-0.203839\pi$
$829$	46.1754	1.60374	0.801868	+	0.597501i	$0.203839\pi$
$830$	−2.45811	−0.0853222
$831$	34.6828	1.20313
$832$	76.1240	2.63912
$833$	−28.2233	−0.977878
$834$	−64.4643	−2.23222
$835$	−2.93127	−0.101441
$836$	−16.6579	−0.576126
$837$	−55.2934	−1.91122
$838$	−81.6081	−2.81910
$839$	−16.3322	−0.563850	−0.281925	−	0.959436i	$-0.590973\pi$
$839$	−16.3322	−0.563850	−0.281925	+	0.959436i	$0.590973\pi$
$840$	0.523334	0.0180567
$841$	16.6817	0.575232
$842$	15.4844	0.533627
$843$	2.54813	0.0877622
$844$	−42.4401	−1.46085
$845$	−16.0249	−0.551272
$846$	−15.3631	−0.528195
$847$	−0.781558	−0.0268547
$848$	−11.1522	−0.382968
$849$	−18.8470	−0.646828
$850$	44.5295	1.52735
$851$	−0.102967	−0.00352966
$852$	8.18294	0.280343
$853$	−38.3110	−1.31174	−0.655872	−	0.754872i	$-0.727699\pi$
$853$	−38.3110	−1.31174	−0.655872	+	0.754872i	$0.727699\pi$
$854$	−5.89548	−0.201739
$855$	1.83358	0.0627072
$856$	12.0761	0.412751
$857$	8.80332	0.300716	0.150358	−	0.988632i	$-0.451957\pi$
$857$	8.80332	0.300716	0.150358	+	0.988632i	$0.451957\pi$
$858$	22.5990	0.771518
$859$	39.2768	1.34011	0.670053	−	0.742313i	$-0.266271\pi$
$859$	39.2768	1.34011	0.670053	+	0.742313i	$0.266271\pi$
$860$	−12.2994	−0.419406
$861$	−12.2114	−0.416164
$862$	−57.6221	−1.96262
$863$	25.6138	0.871905	0.435952	−	0.899970i	$-0.356412\pi$
$863$	25.6138	0.871905	0.435952	+	0.899970i	$0.356412\pi$
$864$	44.6639	1.51950
$865$	7.93418	0.269770
$866$	17.4014	0.591325
$867$	−3.91097	−0.132824
$868$	18.9333	0.642637
$869$	−4.36567	−0.148095
$870$	−10.2948	−0.349027
$871$	72.0363	2.44086
$872$	−11.2646	−0.381467
$873$	1.04879	0.0354962
$874$	1.34975	0.0456559
$875$	−3.55209	−0.120083
$876$	−11.3717	−0.384214
$877$	−10.1716	−0.343470	−0.171735	−	0.985143i	$-0.554937\pi$
$877$	−10.1716	−0.343470	−0.171735	+	0.985143i	$0.554937\pi$
$878$	6.23832	0.210533
$879$	16.9042	0.570165
$880$	−1.35986	−0.0458410
$881$	−37.9802	−1.27959	−0.639793	−	0.768547i	$-0.720980\pi$
$881$	−37.9802	−1.27959	−0.639793	+	0.768547i	$0.720980\pi$
$882$	−7.78254	−0.262052
$883$	−4.78415	−0.160999	−0.0804997	−	0.996755i	$-0.525652\pi$
$883$	−4.78415	−0.160999	−0.0804997	+	0.996755i	$0.525652\pi$
$884$	−74.2716	−2.49803
$885$	−0.706001	−0.0237320
$886$	−4.28753	−0.144042
$887$	40.6272	1.36413	0.682064	−	0.731293i	$-0.261083\pi$
$887$	40.6272	1.36413	0.682064	+	0.731293i	$0.261083\pi$
$888$	1.58211	0.0530923
$889$	8.98236	0.301259
$890$	2.73272	0.0916010
$891$	6.93149	0.232214
$892$	59.8716	2.00465
$893$	−86.1196	−2.88188
$894$	−62.4723	−2.08939
$895$	9.94881	0.332552
$896$	−5.65164	−0.188808
$897$	−1.00623	−0.0335971
$898$	−15.7269	−0.524815
$899$	−67.1142	−2.23838
$900$	6.74741	0.224914
$901$	16.8277	0.560611
$902$	−21.1543	−0.704362
$903$	13.2010	0.439301
$904$	−1.95561	−0.0650428
$905$	6.58705	0.218961
$906$	−34.7843	−1.15563
$907$	−0.368797	−0.0122457	−0.00612285	−	0.999981i	$-0.501949\pi$
$907$	−0.368797	−0.0122457	−0.00612285	+	0.999981i	$0.501949\pi$
$908$	15.7577	0.522938
$909$	−8.32717	−0.276195
$910$	5.27193	0.174763
$911$	13.6707	0.452931	0.226466	−	0.974019i	$-0.427283\pi$
$911$	13.6707	0.452931	0.226466	+	0.974019i	$0.427283\pi$
$912$	31.1083	1.03010
$913$	2.51149	0.0831183
$914$	31.6332	1.04633
$915$	−2.58797	−0.0855557
$916$	52.6783	1.74054
$917$	0.372970	0.0123166
$918$	−51.8282	−1.71059
$919$	10.9742	0.362006	0.181003	−	0.983483i	$-0.442066\pi$
$919$	10.9742	0.362006	0.181003	+	0.983483i	$0.442066\pi$
$920$	−0.0403665	−0.00133084
$921$	−46.0153	−1.51626
$922$	3.08577	0.101624
$923$	14.8542	0.488932
$924$	−2.96729	−0.0976167
$925$	−5.25084	−0.172646
$926$	−24.4155	−0.802344
$927$	0.842807	0.0276814
$928$	54.2122	1.77960
$929$	−3.09566	−0.101565	−0.0507827	−	0.998710i	$-0.516172\pi$
$929$	−3.09566	−0.101565	−0.0507827	+	0.998710i	$0.516172\pi$
$930$	15.1248	0.495962
$931$	−43.6258	−1.42978
$932$	−13.8408	−0.453372
$933$	47.1566	1.54384
$934$	75.2399	2.46192
$935$	2.05192	0.0671048
$936$	−3.69051	−0.120628
$937$	−5.44538	−0.177893	−0.0889463	−	0.996036i	$-0.528350\pi$
$937$	−5.44538	−0.177893	−0.0889463	+	0.996036i	$0.528350\pi$
$938$	−17.2126	−0.562011
$939$	32.6043	1.06400
$940$	14.2929	0.466183
$941$	−3.08325	−0.100511	−0.0502556	−	0.998736i	$-0.516004\pi$
$941$	−3.08325	−0.100511	−0.0502556	+	0.998736i	$0.516004\pi$
$942$	55.2215	1.79921
$943$	0.941907	0.0306727
$944$	2.85910	0.0930559
$945$	2.02157	0.0657616
$946$	22.8686	0.743522
$947$	−7.41852	−0.241070	−0.120535	−	0.992709i	$-0.538461\pi$
$947$	−7.41852	−0.241070	−0.120535	+	0.992709i	$0.538461\pi$
$948$	−16.5748	−0.538326
$949$	−20.6426	−0.670088
$950$	68.8310	2.23317
$951$	−0.547730	−0.0177614
$952$	3.19792	0.103645
$953$	33.8231	1.09564	0.547819	−	0.836597i	$-0.315458\pi$
$953$	33.8231	1.09564	0.547819	+	0.836597i	$0.315458\pi$
$954$	4.64022	0.150233
$955$	3.35277	0.108493
$956$	−49.7831	−1.61010
$957$	10.5184	0.340011
$958$	−45.3443	−1.46501
$959$	7.05179	0.227714
$960$	−7.98467	−0.257704
$961$	67.6020	2.18071
$962$	15.9378	0.513855
$963$	7.53679	0.242870
$964$	−40.4009	−1.30123
$965$	3.31459	0.106700
$966$	0.240432	0.00773579
$967$	48.6831	1.56554	0.782771	−	0.622310i	$-0.213806\pi$
$967$	48.6831	1.56554	0.782771	+	0.622310i	$0.213806\pi$
$968$	−0.926282	−0.0297718
$969$	−46.9397	−1.50792
$970$	−1.77564	−0.0570122
$971$	−13.0405	−0.418488	−0.209244	−	0.977863i	$-0.567100\pi$
$971$	−13.0405	−0.418488	−0.209244	+	0.977863i	$0.567100\pi$
$972$	−14.4379	−0.463096
$973$	15.3649	0.492577
$974$	−56.1968	−1.80066
$975$	−51.3132	−1.64334
$976$	10.4805	0.335474
$977$	17.1476	0.548599	0.274299	−	0.961644i	$-0.411554\pi$
$977$	17.1476	0.548599	0.274299	+	0.961644i	$0.411554\pi$
$978$	44.6750	1.42855
$979$	−2.79207	−0.0892349
$980$	7.24038	0.231286
$981$	−7.03034	−0.224461
$982$	25.7380	0.821333
$983$	51.9784	1.65785	0.828926	−	0.559358i	$-0.188952\pi$
$983$	51.9784	1.65785	0.828926	+	0.559358i	$0.188952\pi$
$984$	−14.4726	−0.461371
$985$	−0.392427	−0.0125038
$986$	−62.9081	−2.00340
$987$	−15.3406	−0.488297
$988$	−114.805	−3.65242
$989$	−1.01823	−0.0323780
$990$	0.565814	0.0179827
$991$	−7.57921	−0.240761	−0.120381	−	0.992728i	$-0.538412\pi$
$991$	−7.57921	−0.240761	−0.120381	+	0.992728i	$0.538412\pi$
$992$	−79.6469	−2.52879
$993$	37.8214	1.20022
$994$	−3.54931	−0.112577
$995$	5.52849	0.175265
$996$	9.53522	0.302135
$997$	−14.3053	−0.453053	−0.226526	−	0.974005i	$-0.572737\pi$
$997$	−14.3053	−0.453053	−0.226526	+	0.974005i	$0.572737\pi$
$998$	−62.6677	−1.98371
$999$	6.11149	0.193359

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.f.1.20	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.f.1.20	✓	121	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.10704 q^{2} -1.55624 q^{3} +2.43961 q^{4} -0.464512 q^{5} +3.27907 q^{6} -0.781558 q^{7} -0.926282 q^{8} -0.578102 q^{9} +O(q^{10})\)	\(q-2.10704 q^{2} -1.55624 q^{3} +2.43961 q^{4} -0.464512 q^{5} +3.27907 q^{6} -0.781558 q^{7} -0.926282 q^{8} -0.578102 q^{9} +0.978744 q^{10} -1.00000 q^{11} -3.79664 q^{12} -6.89190 q^{13} +1.64677 q^{14} +0.722894 q^{15} -2.92751 q^{16} +4.41736 q^{17} +1.21808 q^{18} +6.82809 q^{19} -1.13323 q^{20} +1.21630 q^{21} +2.10704 q^{22} -0.0938169 q^{23} +1.44152 q^{24} -4.78423 q^{25} +14.5215 q^{26} +5.56840 q^{27} -1.90670 q^{28} +6.75883 q^{29} -1.52317 q^{30} -9.92986 q^{31} +8.02095 q^{32} +1.55624 q^{33} -9.30755 q^{34} +0.363043 q^{35} -1.41034 q^{36} +1.09753 q^{37} -14.3871 q^{38} +10.7255 q^{39} +0.430269 q^{40} -10.0398 q^{41} -2.56278 q^{42} +10.8534 q^{43} -2.43961 q^{44} +0.268535 q^{45} +0.197676 q^{46} -12.6125 q^{47} +4.55593 q^{48} -6.38917 q^{49} +10.0806 q^{50} -6.87450 q^{51} -16.8136 q^{52} +3.80944 q^{53} -11.7328 q^{54} +0.464512 q^{55} +0.723943 q^{56} -10.6262 q^{57} -14.2411 q^{58} -0.976632 q^{59} +1.76358 q^{60} -3.58002 q^{61} +20.9226 q^{62} +0.451820 q^{63} -11.0454 q^{64} +3.20137 q^{65} -3.27907 q^{66} -10.4523 q^{67} +10.7767 q^{68} +0.146002 q^{69} -0.764945 q^{70} -2.15531 q^{71} +0.535485 q^{72} +2.99520 q^{73} -2.31254 q^{74} +7.44543 q^{75} +16.6579 q^{76} +0.781558 q^{77} -22.5990 q^{78} +4.36567 q^{79} +1.35986 q^{80} -6.93149 q^{81} +21.1543 q^{82} -2.51149 q^{83} +2.96729 q^{84} -2.05192 q^{85} -22.8686 q^{86} -10.5184 q^{87} +0.926282 q^{88} +2.79207 q^{89} -0.565814 q^{90} +5.38642 q^{91} -0.228877 q^{92} +15.4533 q^{93} +26.5751 q^{94} -3.17173 q^{95} -12.4826 q^{96} -1.81420 q^{97} +13.4622 q^{98} +0.578102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * q^99

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